Sex ratio theory allows unparalleled opportunities for testing how well animal behavior can be predicted by evolutionary theory. For example, Hamilton's theory of local mate competition (LMC) is well understood and can explain variation in sex allocation across numerous species. This allows more specific predictions to be developed and tested. Here we extend LMC theory to a situation that will be common in a range of species: asymmetrical LMC. Asymmetrical LMC occurs when females lay eggs on a patch asynchronously and male offspring do not disperse, leading to relatively weaker LMC for males emerging from later broods. Varying levels of LMC then lead to varying optimal sex ratios for females, depending on when and where they oviposit. We confirm the assumptions of our theory using the wasp Nasonia vitripennis and then test our predictions. We show that females adjust their offspring sex ratios in the directions predicted, laying different sex ratios on different hosts within a patch. Specifically, there was a less female-biased sex ratio when ovipositing on an unparasitized host if another host on the patch had previously been parasitized and a less female-biased sex ratio on parasitized hosts if females also oviposited on an unparasitized host.